Equations Involving Absolute Values
Solving Equations Involving Absolute Values
Solving equations involving absolute values is one of the most important topics in linear equations. In this hub I present several examples with their complete solution. Hope you will find this helpful. This hub presents five sample exercises which demonstrate solving linear equations involving absolute values.
Example one : 3 / X + 5/ = 12
1/3 ( 3 /X + 5/) = 12 (1/3)
/X + 5 / = 4
X + 5 = 4
X = 4 -5 = - 1
X + 5 = -4
X = -4 -5 = -9
Example two : /3X – 1/ + 10 = 25
/3X – 1/ = 25 -10
/ 3X – 1 / = 15
3X – 1 = 15
3X = 15 + 1 = 16
1/3 (3X) = 16 (1/3)
X = 16/3
3X – 1 = -15
3X = -15 + 1
1/3(3X) = -14(1/3)
X = -14/3
Example Three : /3X + 5/ = 5X + 2
3X + 5 = 5X + 2
3X - 5X = 2 - 5
(-1/2)-2X = -3(-1/2)
X = 3/2
3X + 5 = -(5X + 2)
3X + 5 = -5X -2
3X + 5X = -2 -5
(1/8) 8X = -7(1/8)
X = -7/8
Example Four : ½ /3X + 5/ = 6X + 4
2 (1/2 /3X + 5/ ) = (6X + 4 ) 2
/3X + 5 / = 12X + 8
3X + 5 = 12X + 8
3X - 12X = 8 – 5
-9X = 3
(-1/9) -9X = 3 (-1/9)
X = -1/3
3X + 5 = -(12X + 8)
3X + 5 = -12X -8
3X + 12X = -8 -5
(1/15)15X = -13(1/15)
X = -13/15
Example five : 7 /8 – 3X/ = 21X -49
1/7(7 /8-3X/ ) = ( 21X - 49) 1/7
/8 – 3X / = 3X - 7
8 - 3X = 3X - 7
– 3X -3X = -7 -8
(-1/6)-6X = -15 (-1/6)
X = 15/16
8 -3X = -(3X -7)
8 – 3X = -3X + 7
-3X+3X = 7 – 8
0 = -1
No solution